Advances in solid-state chemistry have led to the synthesis of many materials with properties not found in nature but potentially useful in practical applications. A prominent example is high-temperature superconductivity found in synthetic cuprate ceramic materials with superconducting transition temperature, T_c, currently up to 133 K, far exceeding the boiling point of liquid nitrogen, 77.4 K =  -195.8 °C = -320.4 °F, which makes them technologically important since nitrogen is an abundant (78% of air) renewable resource. This discovery was awarded a Nobel Prize in 1987. Detailed studies of these high-T_c superconductors soon revealed that their properties do not fit the established model of superconductivity. In other words, they are impossible under this “conventional” paradigm and were hence termed “unconventional.”  Forty years since their discovery, the microscopic physical mechanism behind their unusual properties (and very high T_c) is still not understood despite an immense body of studies yielding a great deal of knowledge about these materials.  There are many other synthetic unconventional superconductors, such as the heavy-fermions (CeCoIn₅, UPt₃, Ube₁₃, UTe₂, etc.) and more recently discovered iron-based superconductors (e.g., based on BaFe₂As₂, NdFeAsO, FeSe, etc.). There are several thousands of superconducting materials, and by some counts, roughly one-third are unconventional. An important observation is that none of the unconventional superconducting materials or related phases are found in nature (so far).

 Our discovery of unconventional superconductivity in a mineral compound changes this perception and makes us think of the “natural” reasons behind it.

 Twenty-seven chemical elements in the Periodic Table are superconductors at low temperatures and atmospheric pressure.  Since they are all metals that readily react with other elements in Earth’s crust, waters, and atmosphere, it is rare to find pure superconducting elements in nature. Notably, noble metals, such as gold, which can be found in pure form, are not superconducting. And even then, all elemental superconductors are conventional. Multi-element superconducting compounds are even rarer in nature. Only the mineral covellite, CuS, shows superconductivity in samples that occur naturally, a discovery that happened many decades after superconductivity was first detected in laboratory-grown CuS crystals. We know only three other minerals where synthetic analogs are superconductors, namely, parkerite (Ni₃Bi₂S₂), palladseite (Pd₁₇Se₁₅), and miassite (Rh₁₇S₁₅). They all were believed to be conventional.  However, miassite, the subject of our study, turns out to be unconventional, which makes it of particular importance and interest.

 The mineral miassite, initially believed to have Rh₉S₈ composition, was first synthesized in the 1930s, but superconductivity in polycrystals was reported only in 1954. The stoichiometry was refined to Rh₁₇S₁₅ in the early 1960s. This compound has a large unit cell, approximately  1×1×1 nm³, with a complicated structure consisting of two formula units.  A mineral with the same composition was discovered significantly later ( reported only in 2001) in the placers of the Miass River in the Ural Mountains in Russia, from which its name is derived. Natural miassite is found in isoferroplatinum deposits as small rounded inclusions up to 0.1 mm in diameter. As is often the case, natural mineral contains a large amount of impurities, such as iron, nickel, platinum, and copper, at a level of a few atomic percent. This makes studying its intrinsic physical properties difficult, if not impossible; hence, a pure synthetic compound is used.  Figure 1(a) shows one of our lab-grown single crystals of miassite.

 The superconducting properties of miassite display several remarkable features, all pointing to its unconventional nature. Superconductivity is a purely quantum phenomenon. It is achieved when normal electrons pair up into so-called Cooper pairs, forming a superconducting condensate that moves through a crystal lattice without friction and dissipation. In addition to temperature, superconductivity can be destroyed by a magnetic field when it exceeds the so-called upper critical field, H_c2. There are two mechanisms of how it happens. One is due to the precession of Cooper pairs in a magnetic field. When the pair’s Larmor radius, inversely proportional to the magnetic field, becomes comparable to the coherence length, which is the measure of condensate rigidity, the pair breaks up, and the condensate is destroyed. Due to the motion of electrons involved, this mechanism is called orbital upper critical field. The second mechanism is because electron spins in a Cooper pair are anti-parallel. The magnetic field forces all spins to align along its direction via Zeeman interaction. At some critical value, the magnetic field flips one of the spins, and Cooper pairs break up. This is called the Pauli paramagnetic limit.  In most superconductors, the latter is much greater than the former.

Miassite, however, shows anomalously high H_c2, exceeding 20 T at a temperature extrapolated to zero. (For comparison, Earth’s magnetic field is only about 5x10^-5 T and a magnetic field on the surface of a typical strong bar magnet is approximately 2 T). Such high H_c2 is almost two times larger than the Pauli paramagnetic limiting field of about 10 T. So far, no explanation of this observation exists. Other properties, such as large heat capacity jump at T_c, significantly exceeding the predictions of the conventional theory, non-exponential low-temperature variation of heat capacity, and of the nuclear magnetic resonance characteristic time, 1/T₁, are incompatible with a conventional superconductor whose Fermi surface is fully gapped.

 These unusual experimental observations motivated us to study the nature of the superconducting pairing state of Rh₁₇S₁₅ using methods specifically developed for this purpose. Our discovery is based on the measurements of the temperature-dependent London penetration depth and studying the response to a non-magnetic disorder. The London penetration depth is the measure of how far a weak magnetic field (10 million times less than H_c2) penetrates the superconductor interior from the surface. This quantity’s temperature variation is sensitive to how Cooper pairs behave collectively. In conventional superconductors, the London penetration depth is exponentially attenuated when cooling below approximately T_c/3. In stark contrast, it is a T-linear function in unconventional superconductors with line nodes in its order parameter. Figure 1 (b) illustrates these two very different scenarios. We measured the London penetration depth in a dilution refrigerator, a special cryostat reaching 50 mK (~T_c/100), and found a clean linear temperature variation. We have also measured the same crystal in a different apparatus to verify the observations. Figure 1 (b) shows two completely overlapping traces (blue and orange), confirming the reproducibility of our results.

Another independent probe of unconventional superconductivity is its response to non-magnetic disorder.  In conventional superconductors, the transition temperature is practically independent of this type of disorder, and any dependence is due to anisotropy of the superconducting state. However, in the case of a nodal superconductor, T_c is drastically suppressed. The upper critical field is also suppressed, which is only expected in nodal superconductors. Non-magnetic point-like defects in the crystal lattice were introduced by bombarding the sample with 2.5 MeV relativistic electrons. These energetic particles knock out ions of their positions, creating vacancies and interstitials. We observed a significant reduction in the transition temperature at the rate only possible if the order parameter has line nodes.

 We concluded that miassite has an unconventional order parameter with line nodes, similar to high-T_c cuprates. Due to the difference in dimensionality (3D vs. 2D), the nodal structure of miassite is consistent with an extended s-wave state with circular line nodes, which also preserves the cubic symmetry of the crystal. The proposed variation of the superconducting order parameter is shown in Figure 1 (c). Note that red and blue regions have different signs and are separated by (black) circular line nodes where the order parameter is zero.  

 Gap nodes are a hallmark of unconventional superconductivity, observed in high-Tc cuprates, some iron pnictides, heavy-fermions, organic superconductors, and possibly other classes of superconductors. All these materials are products of synthetic chemistry and are not found in nature. Our work establishes Rh₁₇S₁₅ as a unique member of unconventional superconductors, being the only example of a composition that occurs as a natural mineral.  Therefore, our discovery of unconventional superconductivity in Rh₁₇S₁₅ underscores that there is nothing inherently “unnatural” about “unconventional” superconductivity.

 The samples of miassite, Rh17S15, for this project were grown at the US DOE  Ames National Laboratory’s “Complex States, Emergent Phenomena & Superconductivity in Intermetallic & Metal-like compounds” research unit as part of a focused campaign to grow and explore compounds from refractory transition metal (Rh) and volatile element (S) pairs from transition metal-rich eutectics. As the chemical formula implies, this growth is highly challenging, and the conditions should be “just right.” Knowing how difficult this is highlights the importance of our work, which shows that nature is capable of producing some of the most exotic materials.